






"""simple docstring"""





import operator as op


_SCREAMING_SNAKE_CASE   :							Any          =		'''scaler.pt'''
_SCREAMING_SNAKE_CASE   :							Any          =		'''pytorch_model'''
_SCREAMING_SNAKE_CASE   :							Any          =		'''random_states'''
_SCREAMING_SNAKE_CASE   :							Optional[Any]          =		'''optimizer'''
_SCREAMING_SNAKE_CASE   :							Tuple          =		'''scheduler'''
_SCREAMING_SNAKE_CASE   :							int          =		'''pytorch_model.bin'''
_SCREAMING_SNAKE_CASE   :							Union[str, Any]          =		'''pytorch_model.bin.index.json'''
_SCREAMING_SNAKE_CASE   :							Dict          =		'''model.safetensors'''
_SCREAMING_SNAKE_CASE   :							int          =		'''model.safetensors.index.json'''
_SCREAMING_SNAKE_CASE   :							List[str]          =		'''1.10.2'''
_SCREAMING_SNAKE_CASE   :							Tuple          =		'''py38'''
_SCREAMING_SNAKE_CASE   :							int          =		'''4.17.0'''
_SCREAMING_SNAKE_CASE   :							Optional[Any]          =		['''ml.p3.16xlarge''', '''ml.p3dn.24xlarge''', '''ml.p4dn.24xlarge''']
_SCREAMING_SNAKE_CASE   :							Dict          =		['''FULL_SHARD''', '''SHARD_GRAD_OP''', '''NO_SHARD''', '''HYBRID_SHARD''', '''HYBRID_SHARD_ZERO2''']
_SCREAMING_SNAKE_CASE   :							int          =		['''TRANSFORMER_BASED_WRAP''', '''SIZE_BASED_WRAP''', '''NO_WRAP''']
_SCREAMING_SNAKE_CASE   :							str          =		['''BACKWARD_PRE''', '''BACKWARD_POST''', '''NO_PREFETCH''']
_SCREAMING_SNAKE_CASE   :							Tuple          =		['''FULL_STATE_DICT''', '''LOCAL_STATE_DICT''', '''SHARDED_STATE_DICT''']
_SCREAMING_SNAKE_CASE   :							Dict          =		'''2.0.1'''
_SCREAMING_SNAKE_CASE   :							Optional[int]          =		['''pdsh''', '''standard''', '''openmpi''', '''mvapich''']
_SCREAMING_SNAKE_CASE   :							List[Any]          =		['''default''', '''reduce-overhead''', '''max-autotune''']

_SCREAMING_SNAKE_CASE   :							Dict          =		{'''>''': op.gt, '''>=''': op.ge, '''==''': op.eq, '''!=''': op.ne, '''<=''': op.le, '''<''': op.lt}

# These are the args for `torch.distributed.launch` for pytorch < 1.9
_SCREAMING_SNAKE_CASE   :							str          =		[
    '''nnodes''',
    '''nproc_per_node''',
    '''rdzv_backend''',
    '''rdzv_endpoint''',
    '''rdzv_id''',
    '''rdzv_conf''',
    '''standalone''',
    '''max_restarts''',
    '''monitor_interval''',
    '''start_method''',
    '''role''',
    '''module''',
    '''m''',
    '''no_python''',
    '''run_path''',
    '''log_dir''',
    '''r''',
    '''redirects''',
    '''t''',
    '''tee''',
    '''node_rank''',
    '''master_addr''',
    '''master_port''',
]

_SCREAMING_SNAKE_CASE   :							Union[str, Any]          =		['''DEEPSPEED''', '''MULTI_GPU''', '''FSDP''', '''MEGATRON_LM''']
_SCREAMING_SNAKE_CASE   :							List[str]          =		['''DEEPSPEED''', '''MULTI_XPU''', '''FSDP''']












"""simple docstring"""





import functools
from typing import Any







def 	lowerCamelCase__			(				_lowerCamelCase			:						str						,							_lowerCamelCase			:						list[str]					) ->							bool:

  # Validation
  if not isinstance(_lowerCamelCase						,							_lowerCamelCase					) or len(_lowerCamelCase					) == 0:
    raise ValueError('the string should be not empty string'					)

  if not isinstance(_lowerCamelCase						,							_lowerCamelCase					) or not all(
      isinstance(_lowerCamelCase						,							_lowerCamelCase					) and len(_lowerCamelCase					) > 0 for item in words					):
    raise ValueError('the words should be a list of non-empty strings'					)

  # Build trie
  lowerCamelCase_       	=		{}
  lowerCamelCase_       	=		'WORD_KEEPER'

  for word in words:
    lowerCamelCase_       	=		trie
    for c in word:
      if c not in trie_node:
        lowerCamelCase_       	=		{}

      lowerCamelCase_       	=		trie_node[c]

    lowerCamelCase_       	=		True

  lowerCamelCase_       	=		len(_lowerCamelCase					)

  # Dynamic programming method
  @functools.cache
  def is_breakable(_lowerCamelCase			:						int					) -> bool:
    if index == len_string:
      return True

    lowerCamelCase_       	=		trie
    for i in range(_lowerCamelCase						,							_lowerCamelCase					):
      lowerCamelCase_       	=		trie_node.get(string[i]						,							_lowerCamelCase					)

      if trie_node is None:
        return False

      if trie_node.get(_lowerCamelCase						,							_lowerCamelCase					) and is_breakable(i + 1					):
        return True

    return False

  return is_breakable(0					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()




